The equation of the circle passing through the point (1,2) and through the points of intersection of x^2+y^2-4 x-6 y-21=0 and 3 x+4 y+5=0 is given by

Step-by-step solution

Point (1,2) lies on the circle x^2+y^2+2 x+2 y-11=0 , because coordinates of point (1,2) satisfy the equation x^2+y^2+2 x+2 y-11=0 Now, x^2+y^2-4 x-6 y-21=0 ...(i) aligned & x^2+y^2+2 x+2 y-11=0 & 3 x+4 y+5=0 aligned From (i) and (iii), array r x^2+ (- 3 x+5 4 )^2-4 x-6 (- 3 x+5 4 )-21=0 16 x^2+9 x^2+30 x+25-64 x +72 x+120-336=0 array aligned & 25 x^2+38 x-191=0 & From (ii) and (iii), & x^2+ (- 3 x+5 4 )^2+2 x+2 (- 3 x+5 4 )-11=0 & 16 x^2+9 x^2+30 x+25+32 x aligned Thus we get the same equation from (ii) and (iii)